Question icon
Vectors

for what value of k will the set of planes intersect in a line?

x+2y-z=0

x+9y-5z=0

Kx-y+z=0

Profile image of ilham rafie
15 Years agoGrade
Answers icon

1 Answer

Profile image of mounika gajawada
ApprovedApproved Tutor Answer15 Years ago

for three planes to  intersect on a line they gotta have infinite solutions

→ Δ=0 i.e; det of coefficients of planes is 0

→ 1*(9-5)-2*(1+5k)-1(-1-9k)=0

→ k=3